NBHM (National Board for Higher Mathematics) MSc and MA Mathematics: Questions 46 - 53 of 231

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Question 46

Appeared in Year: 2010

Describe in Detail Subjective▾

Let C be the semicircle where varies from , in the complex plane. Evaluate:

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Explanation

Equation of given circle is

… (63 more equations) …

Question 47

Appeared in Year: 2009

Write in Short Short Answer▾

Let

Write down the residues of at each of its poles

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Question 48

Appeared in Year: 2007

Describe in Detail Subjective▾

Let C denote the Boundary of the square whose sides are given by the lines . Assume that C is described in the position sense, i.e.. anticlockwise. Evaluate

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Explanation

Boundary of the Square

To evaluate

Take

H…

… (94 more equations, 12 figures) …

Question 49

Appeared in Year: 2014

Describe in Detail Subjective▾

Let be differentiable at and let . Evaluate

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Explanation

Now

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Question 50

Appeared in Year: 2009

Describe in Detail Subjective▾

Let C be the contour consisting of the lines , described counterclockwise in the plane. Compute

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Explanation

is the contour shown in the figure

The Contour Consisting of the Lines

To evaluate

… (72 more equations, 9 figures) …

Question 51

Appeared in Year: 2017

Describe in Detail Subjective▾

Let Write down the Taylor Expansion of f in the neighbourhood of .

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Explanation

Here

Put

… (68 more equations) …

Question 52

Appeared in Year: 2015

Describe in Detail Subjective▾

In each of the following cases, state whether the given series is absolutely convergent, conditionally convergent or divergent

a)

b)

c)

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Explanation

Option (a) The given series is

Where

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Question 53

Appeared in Year: 2006

Question MCQ▾

Pick out series which are absolutely convergent.

Choices

Choice (4)Response

a.

b.

c.

d.

Both a. and b. are correct

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